Your cycling fallacy is…

“Cycling is not practical or suitable for shopping or for carrying loads”

The response

A standard, practical utility bicycle will have a rear rack and/or a front carrier, which, with the use of pannier bags, can carry a considerable load – and far more easily than walking, as the bicycle is taking the weight, instead of you. These types of bicycle are extremely common in countries like the Netherlands and Denmark, as are cargo bikes, which can carry even larger loads. Shopping by bike is an ordinary, everyday activity.

Of course, it isn't the case that a bicycle has to be used for every single shopping trip. Cars can still be used for larger and heavier loads that would be impractical or impossible to carry by bike. People should still have free choice to use different modes of transport, depending on their needs, requirements and personal choice. But it is not true to say that it is impossible to shop by bike.